The present embodiments relate to a method and a device for determining attenuation coefficients for an object using a movable X-ray source and a detector.
X-ray methods are standard techniques in medical engineering. With simple X-ray photographs, X-ray radiation is transmitted through an object that is to be examined and subsequently recorded by a detector. The recording or projection represents information about the attenuation of the transmitted X-ray beams on a path through the object. The attenuation of the X-ray radiation is dependent on the density of the object parts penetrated by the radiation. The density in turn yields information about the properties of the object, which are typically presented in visual form for diagnostic purposes. In the case of an X-ray photograph, the intensity registered by the detector is dependent on the overall composition of the object along the path traveled by the X-ray beam (i.e., information integrated over a distance is available). Consequently, attenuation coefficients of the object as a function of all three space coordinates are not obtained from a single X-ray photograph. For a three-dimensional image, therefore, a plurality of X-ray photographs are taken from different recording positions, and a three-dimensional image is reconstructed from the plurality of X-ray photographs. In medical engineering, this approach is adopted in computed tomography (CT). Within the framework of computed tomography, the X-ray source and X-ray detector travel along a path or trajectory, and recordings are taken along the trajectory. The recordings are used to reconstruct a three-dimensional image of attenuation coefficients, which relate to the density.
Image reconstruction is a complex, mathematical problem. Two groups of methods have become established for three-dimensional image construction: approximate and exact methods. In this context, theoretically exact methods are methods which, mathematically, include no approximations; the numerical conversion may introduce errors. The approximate methods (e.g., the Feldkamp algorithm) initially had the advantage of the significantly less complex numerical conversion. Thanks to skillful formulations of the mathematical problem, which have been proposed in the last several years, there is now available a theoretically exact formulation, which can be converted numerically with a realistic amount of effort. This is described, for example, in U.S. Pat. No. 6,771,733 B2. U.S. Pat. No. 6,771,733 B2 discloses a reconstruction formula (formula 10), which is well suited to the numerical conversion of an exact method. For implementation, this reconstruction formula generally makes use of a further transformation according to the path or trajectory used. The corresponding formula for a spiral path is expressed, for example, in the cited publication as formula 29.
In respect of the numerical conversion, however, difficulties continue to exist. One challenge that remains is finding a reasonable compromise between the number of projections recorded and the image quality, the image quality generally being higher, the more images that are recorded. However, it is also desirable to limit the number of recordings made in order to limit the exposure to radiation of patients being examined.